Watching The Arsenal last night reminded me of a saying by Niels Bohr and Jon Elster - that the opposite of a great truth is sometimes another great truth.

What I mean is that some Gooners have long been critical of Olivier Giroud and have called for the signing of a big-name striker. But what sort of things could a top-class striker do? Pull back a two-goal deficit against a top team away from home, that's what...which is exactly what Giroud did. Had a new £50m signing turned the game as he did, everyone would be saying today what a fantastic signing he was.

To some degree, Giroud is a victim of the phenomenon described in those old sayings, familiarity breeds contempt and the grass is greener. Sometimes, we undervalue what is known and familiar to us, and overvalue what we don't have. As Joni Mitchell said, you don't what you've got till it's gone.

Gooners are of course not unusual in this regard. Last Christmas, when West Ham were in the relegation zone, some Irons wanted Sam Allardyce sacked. But then it was pointed out that the sort of manager West Ham needed was just the sort that Mr Allardyce was. He stayed, and the Hammers have since improved.

The grass is greener/familiarity breeds contempt effects help explain why fans often want their manager sacked (though of course sometimes the calls are rational), and why we get so excited on transfer deadline day - because the players we are about to sign are more thrilling than the ones we actually have. They also explain why men cheat on their wives, somtimes with unhappy effects (as Olivier himself knows).

So far, so obvious. But here's where Bohr and Elster's saying comes in. The opposite phenomenon also exists. Sometimes, we overvalue things simply by virtue of owning them; the endowment effect has been established in laboratory experiments (pdf). This helps explain a range of behaviour such as why housing transactions tend to slump when prices fall (because homeowners overvalue their houses and so set too high a reservation price) or why people tolerate inequality - it's (partly) because they over-rate the merits of existing inequality.

What we have here, then, is something that is quite common in the social sciences. We have two opposing mechanisms, which poses the question: in what circumstances will one mechanism be more powerful than its opposite?

Often, this question can only be answered in hindsight: as Elster stressed, prediction and explanation are two different things.

There is, though, (at least) one circumstance relevant to our case - aspirations. Demands for social change tend to be greatest not so much when people are abjectly poor and oppressed, but rather when their aspirations are higher than their objective conditions. It is then that the grass is greener effect outweighs the endowment effect. This helps explain discontent with Giroud. It those Gooners who expect Arsenal to win the league who are most unhappy with him, whilst those with lower expectations see his merits.

I've said it before, and I'll keep saying it: football can illuminate important issues in the social sciences.